Preparation of thermoplastic rubber compositions by use of so-called dynamic crosslinking reaction, in which a radical-crosslinkable olefinic rubber and a non-radical-crosslinkable olefinic resin such as polypropylene (PP) are crosslinked in the presence of a radical polymerization initiator while being melted and mixed in an extruder, is a technique already known in the art and widely used for the manufacture of automobile parts, etc.
As said type of olefinic rubber, there are known ethylene-propylene-diene rubber (EPDM) compositions and olefinic elastomer compositions produced by using a metallocene catalyst (JP-A-8-120127, JP-A-9-137001, JP-A-9-104787 and JP-A-10-87912). These known compositions, however, are not necessarily satisfactory in mechanical strength, and quest has been made for the olefinic rubber compositions which can stand practical use.